Looking for opinions on best way to achieve couch gaming using a PC/Controller/TV

So I was hoping that Shield would be able to solve my use case problem, but it doesn't look like it.

What I've got is a Z0tac HD-ID11 (Ubuntu) hooked up to my TV. This is connected via gigabit network to my main desktop (Win7) on the other side of the room.

What I'd like to do, is be able to use my desktop for cpu/gpu, but have the output sent to my TV.

Wired HDMI isn't an option, as 1) I'd rather not have to connect/disconnect a cable from my video card as I'm already using both outputs, and more importantly, 2) I don't want to run a 20 foot cable across the living room.

Are there any solutions or devices out there that work over gigabit ethernet that would enable me to stream the output from my desktop to either the zotac or another specific device? Either by capturing the active audio/video from a single monitor, or psuedo display output that I could redirect to to stream it.

Or as a backup, a wireless hdmi solution that can handle 1920x1080 / 5 channel sound without noticeable degradation?